Here \(\vec{x}_k\)  denote the positions of the gravitating masses, \(\vec{j}_k\)  the associated Schwinger
parameters, \(S_{pp}\)  the point particle action, Eq. (10) [1]}, \({\cal L}_{\rm int}\) 
the interaction Lagrangian density, \(J_i\)  are the Schwinger parameters to \(\Phi _i\) ,
with
\(\delta _{J_k} \equiv \frac{\delta }{\delta J_k},\) 
